Can I make it always night time?

As of 0.16.0, you can change the time to night one time by

/time set night

To make it night constantly, (or if you are on lower versions then 0.16) you can use a mod:

• Simple Commands mod

  Simple Commands mod adds a few new, simple text commands. Now, among the "standard" commands will have a new command that has the effect to your character. In total there are 23 different effects, such as speed and invisibility - it is the effects of potions. With these commands, you can affect the gamegame mode, weather, time, deceleration time, set the level of experience, and more in MCPE 0.11-0.15.7

• pocketInvEditor mod (available on Google Play)

  PocketInvEditor is an inventory editor for Minecraft Pocket Edition. With this tool, you can give yourself more blocks and items without writing a single hexadecimal digit or connecting to a computer.

  • the mod also allows locking the day/night cycle

It seems that as of the 1.1 update "The Discovery Update" (June 1st, 2017), it is possible with the gamerule doDaylightCycle. The command:

/gamerule doDaylightCycle false

will stop the cycle from day to night and night to day. Just use it when it is night. I believe that will do the trick.

Not possible without a mod. This is a good one:

http://mcpeuniverse.com/mods/always-night/